10 papers
Squared polynomial approximation kernels for the hypercube: improved error bounds and implications for Lasserre hierarchies
Sander Gribling, Etienne de Klerk, Juan C. Vera
We propose a new family of polynomial approximation kernels for approximating nonnegative polynomials on the hypercube . Our Kernels produce polynomial sums-of-squares of…
Degree Bounds for Positivstellensätze of general semialgebraic sets
Olga Heijmans-Kuryatnikova, Juan C. Vera, Luis F. Zuluaga
Let denote the minimum of a polynomial over a (general) compact semialgebraic set . A standard way to approximate is via hierarc…
Linear Convergence and Error Bounds for Optimization Without Strong Convexity
Kira van Treek, Javier F. Peña, Juan C. Vera +1
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterat…
Low degree sum-of-squares bounds for the stability number: a copositive approach
Luis Felipe Vargas, Juan C. Vera, Peter J. C. Dickinson
The stability number of a graph , denoted as , is the maximum size of an independent (stable) set in . Semidefinite programming (SDP) methods, which originated from Lov…
SDP bounds on the stability number via ADMM and intermediate levels of the Lasserre hierarchy
Lennart Sinjorgo, Renata Sotirov, Juan C. Vera
We consider the Lasserre hierarchy for computing bounds on the stability number of graphs. The semidefinite programs (SDPs) arising from this hierarchy involve large matrix variabl…
Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube
Sander Gribling, Etienne de Klerk, Juan Vera
We revisit the problem of minimizing a given polynomial on the hypercube . Lasserre's hierarchy (also known as the moment- or sum-of-squares hierarchy) provides a seq…
Lagrangian Reformulation for Nonconvex Optimization: Tailoring Problems to Specialized Solvers
Rodolfo A. Quintero, Juan C. Vera, Luis F. Zuluaga
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This…
The link between -norm approximation and effective Positivstellensatze for the hypercube
Etienne de Klerk, Juan Vera Lizcano
The Schmüdgen's Positivstellensatz gives a certificate to verify positivity of a strictly positive polynomial on a compact, basic, semi-algebraic set $\mathbf{K} \subset \mathb…
Duality of Hoffman constants
Javier F. Pena, Juan C. Vera, Luis F. Zuluaga
We show that a suitable Slater condition implies a duality inequality between the Hoffman constants of the following feasibility problems: $$ \begin{array}{r} Ax-b \in S\\ x \in R…
Sparse non-SOS Putinar-type Positivstellensätze
Lorenz M. Roebers, Juan C. Vera, Luis F. Zuluaga
Recently, non-SOS Positivstellensätze for polynomials on compact semialgebraic sets, following the general form of Schmüdgen's Positivstellensatz, have been derived by appropriatel…